Extra Storage Space
If I want to add only more hardrive space will it effect the up time of the server?
Second, how can this be done so that our Plesk server will make use of the space
There are a few ways of adding more storage space, and I'll go over them here.
The first is to resize your Linode. Keep in mind that when switching to a higher plan, the other aspects of the plan (CPU Cores, Transfer, etc.) go up as well. Also, when you switch plans the pricing goes up as well. I'm attaching two links below, one that shows you the pricing and plans and the other shows you how to resize a Linode:
Resizing a Linode will give you a period of downtime because it will require your Linode to be powered down and migrated to a different host in the same data center during the resize process.
Now, since you're only looking to add extra storage space, your best bet might be to add a Block Storage Volume. It will only give you extra storage space and you can attach it and detach it to your Linode at will. A rule of thumb to remember is that it would need to be in the same data center as your Linode.
A Block Storage Volume will not affect your Linode's uptime unless you choose to detach it, in which case your Linode will need to be powered down.
Once the Block Storage Volume is attached, you'll be able to utilize that extra space on your Plesk server and you can partition it any way you'd like to accommodate any type of file system that you choose.